Average Error: 0.0 → 0.0
Time: 26.9s
Precision: binary64
Cost: 13184
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[{\left(e^{-1}\right)}^{\left(1 - x \cdot x\right)}\]
e^{-\left(1 - x \cdot x\right)}
↓
{\left(e^{-1}\right)}^{\left(1 - x \cdot x\right)}
(FPCore (x) :precision binary64 (exp (- (- 1.0 (* x x)))))
↓
(FPCore (x) :precision binary64 (pow (exp -1.0) (- 1.0 (* x x))))
double code(double x) {
	return exp(-(1.0 - (x * x)));
}
↓
double code(double x) {
	return pow(exp(-1.0), (1.0 - (x * x)));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Alternatives

Alternative 1
Error0.0
Cost6720
\[e^{-1 + x \cdot x}\]
Alternative 2
Error0.6
Cost1088
\[\frac{1 - \left(x \cdot x\right) \cdot \left(x \cdot x\right)}{\left(1 - x \cdot x\right) \cdot e}\]
Alternative 3
Error0.6
Cost576
\[\frac{1}{\frac{e}{1 + x \cdot x}}\]
Alternative 4
Error0.6
Cost448
\[\frac{1 + x \cdot x}{e}\]
Alternative 5
Error52.6
Cost64
\[1\]

Error

Time

Derivation

  1. Initial program 0.0

    \[e^{-\left(1 - x \cdot x\right)}\]
  2. Using strategy rm

  3. Applied neg-mul-1_binary64_740.0

    \[\leadsto e^{\color{blue}{-1 \cdot \left(1 - x \cdot x\right)}}\]

  4. Applied exp-prod_binary64_1300.0

    \[\leadsto \color{blue}{{\left(e^{-1}\right)}^{\left(1 - x \cdot x\right)}}\]

  5. Simplified0.0

    \[\leadsto \color{blue}{{\left(e^{-1}\right)}^{\left(1 - x \cdot x\right)}}\]

  6. Final simplification0.0

    \[\leadsto {\left(e^{-1}\right)}^{\left(1 - x \cdot x\right)}\]

Reproduce

herbie shell --seed 2021040 
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (- (- 1.0 (* x x)))))